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Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy–Rees technique

François Béguin[1]; Sylvain Crovisier; Frédéric Le Roux

  • [1] École Normale Supérieure de Lyon, UMPA, 46 allée d'Italie, 69364 Lyon Cedex 07 (France)

Annales scientifiques de l'École Normale Supérieure (2007)

  • Volume: 40, Issue: 2, page 251-308
  • ISSN: 0012-9593

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Béguin, François, Crovisier, Sylvain, and Le Roux, Frédéric. "Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy–Rees technique." Annales scientifiques de l'École Normale Supérieure 40.2 (2007): 251-308. <http://eudml.org/doc/82713>.

@article{Béguin2007,
affiliation = {École Normale Supérieure de Lyon, UMPA, 46 allée d'Italie, 69364 Lyon Cedex 07 (France)},
author = {Béguin, François, Crovisier, Sylvain, Le Roux, Frédéric},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {representation by homeomorphisms on manifolds; control the measurable dynamics; measurable dynamical systems},
language = {eng},
number = {2},
pages = {251-308},
publisher = {Elsevier},
title = {Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy–Rees technique},
url = {http://eudml.org/doc/82713},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Béguin, François
AU - Crovisier, Sylvain
AU - Le Roux, Frédéric
TI - Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy–Rees technique
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2007
PB - Elsevier
VL - 40
IS - 2
SP - 251
EP - 308
LA - eng
KW - representation by homeomorphisms on manifolds; control the measurable dynamics; measurable dynamical systems
UR - http://eudml.org/doc/82713
ER -

References

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  1. [1] Anosov D., Katok A., New examples in smooth ergodic theory. Ergodic diffeomorphisms, Trans. Moscow Math. Soc.23 (1970) 1-35. Zbl0255.58007MR370662
  2. [2] Béguin F., Crovisier S., Le Roux F., Patou A., Pseudo-rotations of the closed annulus: variation on a theorem of J. Kwapisz, Nonlinearity17 (4) (2004) 1427-1453. Zbl1077.37032MR2069713
  3. [3] Béguin F., Crovisier S., Le Roux F., Pseudo-rotations of the open annulus: variation on a theorem of J. Kwapisz, Bull. Braz. Math. Soc. (N.S.)37 (2006) 275-306. Zbl1105.37029MR2266384
  4. [4] Béguin F., Crovisier S., Jaeger T., Le Roux F., Denjoy constructions for fibered homeomorphism of the two-torus, in preparation. 
  5. [5] Bing R.H., Tame Cantor sets in E 3 , Pacific J. Math.11 (1961) 435-446. Zbl0111.18606MR130679
  6. [6] Bing R.H., The Geometric Topology of 3-Manifolds, American Mathematical Society Colloquium Publications, vol. 40, American Mathematical Society, Providence, RI, 1983. Zbl0535.57001MR728227
  7. [7] Brown M., A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc.66 (1960) 74-76. Zbl0132.20002MR117695
  8. [8] Denjoy A., Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. Ser. IX11 (1932) 333-375. Zbl0006.30501
  9. [9] Denker M., Grillenberger C., Sigmund K., Ergodic Theory on Compact Spaces, Springer Lecture Notes in Math., vol. 527, Springer-Verlag, Berlin/New York, 1976. Zbl0328.28008MR457675
  10. [10] Fathi A., Herman M., Existence de difféomorphismes minimaux, in: Dynamical Systems, vol. I, Warsaw, Astérisque, vol. 49, Soc. Math. France, Paris, 1977, 37–59. Zbl0374.58010
  11. [11] Fayad B., Katok A., Constructions in elliptic dynamics, Ergodic Theory Dynam. Systems24 (5) (2004) 1477-1520. Zbl1089.37012MR2104594
  12. [12] Handel M., A pathological area preserving C diffeomorphism of the plane, Proc. Amer. Math. Soc.86 (1) (1982) 163-168. Zbl0509.58031MR663889
  13. [13] Herman M., Construction d'un difféomorphisme minimal d'entropie topologique non-nulle, Ergodic Theory Dynam. Systems1 (1981) 65-76. Zbl0469.58008MR627787
  14. [14] Herman M., Construction of some curious diffeomorphisms of the Riemann sphere, J. London Math. Soc. (2)34 (2) (1986) 375-384. Zbl0603.58017MR856520
  15. [15] Homma T., On tame imbedding of 0-dimensional compact sets in E 3 , Yokohama Math. J.7 (1959) 191-195. Zbl0094.36005MR124037
  16. [16] Jäger T., Stark J., Towards a classification for quasi-periodically forced circle homeomorphisms, J. London Math. Soc.73 (2006) 727-744. Zbl1095.37013MR2241977
  17. [17] Katok A., Lyapounov exponents, entropy and periodic orbits for diffeomorphisms, Publications Mathématiques de l'I.H.É.S.51 (1980) 131-173. Zbl0445.58015MR573822
  18. [18] Le Calvez P., Rotation numbers in the infinite annulus, Proc. Amer. Math. Soc.129 (11) (2001) 3221-3230. Zbl0990.37029MR1844997
  19. [19] Lind D., Thouvenot J.-P., Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations, Math. Systems Theory11 (3) (1977/78) 275-282. Zbl0377.28011MR584588
  20. [20] Osborne R.P., Embedding Cantor sets in a manifold. I. Tame Cantor sets in E n , Michigan Math. J.13 (1966) 57-63. Zbl0138.18902MR187225
  21. [21] Oxtoby J.C., Ulam S.M., Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2)42 (1941) 874-920. Zbl0063.06074MR5803
  22. [22] Rees M., A minimal positive entropy homeomorphism of the 2-torus, J. London Math. Soc.23 (1981) 537-550. Zbl0451.58022MR616561
  23. [23] Sanford M.D., Walker R.B., Extending maps of a Cantor set product with an arc to near homeomorphisms of the 2-disk, Pacific J. Math.192 (2) (2000) 369-384. Zbl1092.37502MR1744576
  24. [24] Thouvenot J.-P., Entropy, isomorphisms and equivalence, in: Katok A., Hasselblatt B. (Eds.), Handbook of Dynamical Systems, vol. 1A, Elsevier, Amsterdam, 2002. Zbl1084.37007MR1928517

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